NUMERICAL STUDY OF MULTISCALE CAVITATING FLOW AROUND A HYDROFOIL
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摘要: 空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.Abstract: The multiscale effect of cavitation is a complex hydrodynamic phenomenon involving macroscale cavitation, microscale cavitation bubbles and transformation between scales. The cavitating flow around a NACA66 hydrofoil is simulated based on the established Euler-Lagrange algorithm. The macroscale cavitation vapor was captured through a large eddy simulation (LES) method and the volume of fluid (VOF) method in an Eulerian analysis. The motion, growth and collapse of sub-grid scale discrete bubbles were solved through discrete bubble model (DBM) in Lagrangian frame. Meanwhile, the solution model of different scale cavitation is selected through the comparison of scale between cavitation cavity and the local grid. The experimental results are compared with the numerical results to verify the accuracy of the numerical method. The results show that the number of discrete bubbles is closely related to the development of cloud cavitation. The number of discrete bubbles fluctuate little in the growth stage of attached sheet cavity with the bubbles mainly distributed at the interface of water and vapour. With the re-entrant jet occur at the trailing edge of attached cavity and develop to leading edgy of hydrofoil, the bubble number gradually increase and fill up the jet disturbance region. When the cavity detach, converge and shed downstream along with the hydrofoil, the discrete bubble number increase rapidly and the bubbles dispersed in the mixing region of water and vapour. Moreover, the probability density function of discrete bubble diameter conforms to Gamma distribution for the whole stage of cloud cavitation. With the increase of cavitation diameter, the number of cavitation first increases and then decreases. Additionally, the characteristics of the cavitation turbulent flow field have an important influence on the distribution of bubbles, and the discrete bubble is mainly distributed in the region of strong turbulence intensity, vortex and re-entrant flow.
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Key words:
- cavitation /
- multiscale /
- Euler-Lagrange /
- interface capturing method /
- discrete bubble model
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图 1 欧拉−拉格朗日转换过程动量源项耦合示意图
Figure 1. Schematic of the process of the momentum source term coupling during Euler−Lagrange transforms
图 5 相同计算时刻水翼吸力面y+ 分布
Figure 5. The y+ value distributions on the suction side of hydrofoil at the same calculation time
图 6 典型周期绕水翼多尺度空泡时空演化(气相体积分数αv = 0.1)
Figure 6. Spatial-temporal evolution of multiscale cavitation around hydrofoil on typical period (αv = 0.1)
图 7 空泡欧拉−拉格朗日多尺度转化及演变过程
Figure 7. The process of transition and evolution between Euler−Lagrangian frame of bubble
图 8 水翼升力系数及振动位移频谱对比
Figure 8. Comparison of lift coefficient and vibration displacement spectrum of hydrofoil
图 11 离散空泡群索特直径及微尺度空泡期望直径随时间变化曲线
Figure 11. Sauter diameter of discrete cavitation group and expected diameter of microscale bubble verse time
图 12 附着型空泡生长阶段不同尺度离散空泡数概率密度分布云图
Figure 12. The probability density of discrete cavitation numbers at different scales during the stage of the growth of attached cavity
图 13 回射流发展阶段不同尺度离散空泡数概率密度分布云图
Figure 13. The probability density of discrete cavitation numbers at different scales during the stage of the development of re-entrant jet
图 14 云状空化脱落阶段不同尺度离散空泡数概率密度沿水翼分布云图
Figure 14. The probability density of discrete cavitation numbers at different scales during the stage of the cloud sheds
15 附着型空泡生长阶段湍流流场特性
15. Characteristics of turbulent flow field during the stage of the growth of attached cavity
15 附着型空泡生长阶段湍流流场特性(续)
15. Characteristics of turbulent flow field during the stage of the growth of attached cavity (continued)
16 云状空化脱落阶段不同尺度离散空泡数概率密度沿水翼分布云图
16. The probability density of discrete cavitation numbers at different scales during the stage of the cloud sheds
16 云状空化脱落阶段不同尺度离散空泡数概率密度沿水翼分布云图(续)
16. The probability density of discrete cavitation numbers at different scales during the stage of the cloud sheds (continued)
17 云状空化脱落阶段湍流流场特性
17. Characteristics of turbulent flow field during the stage of the cloud sheds
17 云状空化脱落阶段湍流流场特性(续)
17. Characteristics of turbulent flow field during the stage of the cloud sheds (continued)
表 1 网格数、
$x^+ $ 及$z^+ $ 值Table 1. Number of grids, x+ and
$z^+$ valuesGrid number/106 x + z + MeshⅠ 2.35 220 52 MeshⅡ 4.7 89 22.5 Mesh Ⅲ 6.7 75 16 
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